Write a rule for the function represented by the table.
x y
0 14
1 29
2 44
3 59
bruh what just give the answers tf??
Straight line equations:
y = mx + b
m = slope
b = y-intercept ( Point on the graph where x is zero )
Difference between y coordinates is constant = 15
29 - 14 = 15
44 - 29 = 15
59 - 44 = 15
Slope = 15
y-intercept = y coordinate when x = 0
y-intercept = 14
So :
m = 15
b = 14
y = mx + b
y = 15 x + 14
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Itβs y = 15 + 14x :))
Rule: The function takes the given input value of 'x' and multiplies it by 15, then adds 14 to it. So, the rule for this function is y = 15x + 14. Just like how adding clown makeup makes everything funnier, adding 14 makes these numbers more interesting.
To write a rule for the function represented by the table, we need to find a pattern or relationship between the x-values and y-values. Let's examine the differences between the x-values and y-values.
If we look at the differences between the x-values, we can see that they are all increasing by 1 each time: 1 - 0 = 1, 2 - 1 = 1, and 3 - 2 = 1. This tells us that there is a linear relationship between the x-values and y-values.
Now let's look at the differences between the y-values. The differences are 29 - 14 = 15, 44 - 29 = 15, and 59 - 44 = 15. The differences between the y-values are the same each time, which indicates that the relationship between the x-values and y-values is also linear.
We can conclude that the relationship between the x-values and y-values is a linear relationship with a constant difference of 15.
To find the rule, we start with the general equation for a linear relationship: y = mx + b, where m represents the slope and b represents the y-intercept.
Since we have established that the difference between the y-values is 15, we can determine that the slope (m) is 15.
To find the y-intercept (b), we can substitute any point from the table into the equation and solve for b. Let's choose the point (0, 14):
14 = 15(0) + b
14 = 0 + b
b = 14
Now that we have the values for m and b, we can write the final rule for the function represented by the table as:
y = 15x + 14
X= -1/0/1/2/1
Y=80/40/20/10/5